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      "cell_type": "code",
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        "%matplotlib inline"
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        "\nPyTorch: Tensors and autograd\n-------------------------------\n\nA third order polynomial, trained to predict $y=\\sin(x)$ from $-\\pi$\nto $pi$ by minimizing squared Euclidean distance.\n\nThis implementation computes the forward pass using operations on PyTorch\nTensors, and uses PyTorch autograd to compute gradients.\n\n\nA PyTorch Tensor represents a node in a computational graph. If ``x`` is a\nTensor that has ``x.requires_grad=True`` then ``x.grad`` is another Tensor\nholding the gradient of ``x`` with respect to some scalar value.\n\n"
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    {
      "cell_type": "code",
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      "source": [
        "import torch\nimport math\n\ndtype = torch.float\ndevice = torch.device(\"cpu\")\n# device = torch.device(\"cuda:0\")  # Uncomment this to run on GPU\n\n# Create Tensors to hold input and outputs.\n# By default, requires_grad=False, which indicates that we do not need to\n# compute gradients with respect to these Tensors during the backward pass.\nx = torch.linspace(-math.pi, math.pi, 2000, device=device, dtype=dtype)\ny = torch.sin(x)\n\n# Create random Tensors for weights. For a third order polynomial, we need\n# 4 weights: y = a + b x + c x^2 + d x^3\n# Setting requires_grad=True indicates that we want to compute gradients with\n# respect to these Tensors during the backward pass.\na = torch.randn((), device=device, dtype=dtype, requires_grad=True)\nb = torch.randn((), device=device, dtype=dtype, requires_grad=True)\nc = torch.randn((), device=device, dtype=dtype, requires_grad=True)\nd = torch.randn((), device=device, dtype=dtype, requires_grad=True)\n\nlearning_rate = 1e-6\nfor t in range(2000):\n    # Forward pass: compute predicted y using operations on Tensors.\n    y_pred = a + b * x + c * x ** 2 + d * x ** 3\n\n    # Compute and print loss using operations on Tensors.\n    # Now loss is a Tensor of shape (1,)\n    # loss.item() gets the scalar value held in the loss.\n    loss = (y_pred - y).pow(2).sum()\n    if t % 100 == 99:\n        print(t, loss.item())\n\n    # Use autograd to compute the backward pass. This call will compute the\n    # gradient of loss with respect to all Tensors with requires_grad=True.\n    # After this call a.grad, b.grad. c.grad and d.grad will be Tensors holding\n    # the gradient of the loss with respect to a, b, c, d respectively.\n    loss.backward()\n\n    # Manually update weights using gradient descent. Wrap in torch.no_grad()\n    # because weights have requires_grad=True, but we don't need to track this\n    # in autograd.\n    with torch.no_grad():\n        a -= learning_rate * a.grad\n        b -= learning_rate * b.grad\n        c -= learning_rate * c.grad\n        d -= learning_rate * d.grad\n\n        # Manually zero the gradients after updating weights\n        a.grad = None\n        b.grad = None\n        c.grad = None\n        d.grad = None\n\nprint(f'Result: y = {a.item()} + {b.item()} x + {c.item()} x^2 + {d.item()} x^3')"
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